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Modeling aerospace trajectories requires positioning and orienting the aircraft or spacecraft with respect to the rotating Earth. Navigation coordinates are defined with respect to the center and surface of the Earth.

### Geocentric and Geodetic Latitudes

The geocentric latitude λ on the Earth surface is defined by the angle subtended by the radius vector from the Earth center to the surface point with the equatorial plane.

The geodetic latitude μ on the Earth surface is defined by the angle subtended by the surface normal vector `n` and the equatorial plane. ### NED Coordinates

The north-east-down (NED) system is a noninertial system with its origin fixed at the aircraft or spacecraft's center of gravity. Its axes are oriented along the geodetic directions defined by the Earth surface.

• The `x`-axis points north parallel to the geoid surface, in the polar direction.

• The `y`-axis points east parallel to the geoid surface, along a latitude curve.

• The `z`-axis points downward, toward the Earth surface, antiparallel to the surface's outward normal `n`.

Flying at a constant altitude means flying at a constant `z` above the Earth's surface. ### ECI Coordinates

The Earth-centered inertial (ECI) system is non-rotating. For most applications, assume this frame to be inertial, although the equinox and equatorial plane move very slightly over time. The ECI system is considered to be truly inertial for high-precision orbit calculations when the equator and equinox are defined at a particular epoch (e.g. J2000). Aerospace functions and blocks that use a particular realization of the ECI coordinate system provide that information in their documentation. The ECI system origin is fixed at the center of the Earth (see figure).

• The x-axis points towards the vernal equinox (First Point of Aries ♈).

• The y-axis points 90 degrees to the east of the x-axis in the equatorial plane.

• The z-axis points northward along the Earth rotation axis.

Earth-Centered Coordinates ### ECEF Coordinates

The Earth-center, Earth-fixed (ECEF) system is a noninertial system that rotates with the Earth. Its origin is fixed at the center of the Earth.

• The `z`-axis points northward along the Earth's rotation axis.

• The `x`-axis points outward along the intersection of the Earth's equatorial plane and prime meridian.

• The `y`-axis points into the eastward quadrant, perpendicular to the `x`-`z` plane so as to satisfy the RH rule.

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